# Number System

 Question 1
Consider three floating point numbers A, B and C stored in registers $R_A$, $R_B$ and $R_C$, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

$R_A=0xC1400000$
$R_B=0x42100000$
$R_C=0x41400000$

Which one of the following is FALSE?
 A $A+C=0$ B $C=A+B$ C $B=3C$ D $(B-C) \gt 0$
GATE CSE 2022   Digital Logic
Question 1 Explanation:
 Question 2
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
 A R1 = 1011 and R2 = 1110 B R1 = 1100 and R2 = 1010 C R1 = 0011 and R2 = 0100 D R1 = 1001 and R2 = 1111
GATE CSE 2022   Digital Logic
Question 2 Explanation:
 Question 3
If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?
[MSQ]
 A 0x6665 B 0x0001 C 0x4243 D 0x0100
GATE CSE 2021 SET-2   Digital Logic
Question 3 Explanation:
 Question 4
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
 A 3 B 6 C 8 D 4
GATE CSE 2021 SET-2   Digital Logic
Question 4 Explanation:
 Question 5
The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows:

$\begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}$

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
 A exponent = 00000000 and mantissa = 0000000000000000000000000 B exponent = 00000000 and mantissa = 0000000000000000000000001 C exponent = 00000001 and mantissa = 0000000000000000000000000 D exponent = 00000001 and mantissa = 0000000000000000000000001
GATE CSE 2021 SET-2   Digital Logic
Question 5 Explanation:
 Question 6
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1
E:10000001
F:11110000000000000000000

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
 A -7.75 B 7.75 C -3.825 D 3.825
GATE CSE 2021 SET-1   Digital Logic
Question 6 Explanation:
 Question 7
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
 A 15 B 21 C D2 D 528
GATE CSE 2021 SET-1   Digital Logic
Question 7 Explanation:
 Question 8
Consider three registers R1, R2, and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.

If $R3=\frac{R1}{R2}$, what is the value stored in R3?
 A 0x40800000 B 0xC0800000 C 0x83400000 D 0xC8500000
GATE CSE 2020   Digital Logic
Question 8 Explanation:
 Question 9
Consider Z = X - Y where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:
 A n bits B n-1 bits C n+1 bits D n+2 bits
GATE CSE 2019   Digital Logic
Question 9 Explanation:
 Question 10
In 16-bit 2's complement representation, the decimal number -28 is:
 A 1111 1111 0001 1100 B 0000 0000 1110 0100 C 1111 1111 1110 0100 D 1000 0000 1110 0100
GATE CSE 2019   Digital Logic
Question 10 Explanation:
There are 10 questions to complete.